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THE THEORY OF EVERYTHING
The Origin and Fate of the Universe
By Stephen W. Hawking
NEW MILLENNIUM PRESS
Copyright © 2002 New Millennium Press.
All rights reserved.
ISBN: 1893224546
Chapter One
As long ago as 340 B.C. Aristotle, in his book On the Heavens, was able to put forward two good arguments for believing that the Earth was a round ball rather than a flat plate. First, he realized that eclipses of the moon were caused by the Earth coming between the sun and the moon. The Earth's shadow on the moon was always round, which would be true only if the Earth was spherical. If the Earth had been a flat disk, the shadow would have been elongated and elliptical, unless the eclipse always occurred at a time when the sun was directly above the center of the disk.
Second, the Greeks knew from their travels that the Pole Star appeared lower in the sky when viewed in the south than it did in more northerly regions. From the difference in the apparent position of the Pole Star in Egypt and Greece, Aristotle even quoted an estimate that the distance around the Earth was four hundred thousand stadia. It is not known exactly what length a stadium was, but it may have been about two hundred yards. This would make Aristotle's estimate about twice the currently accepted figure.
The Greeks even had a third argument that the Earth must be round, for why else does one first see the sails of a ship coming over the horizon and only later see the hull? Aristotle thought that the Earth was stationary and that the sun, the moon, the planets, and the stars moved in circular orbits about the Earth. He believed this because he felt, for mystical reasons, that the Earth was the center of the universe and that circular motion was the most perfect.
This idea was elaborated by Ptolemy in the first century A.D. into a complete cosmological model. The Earth stood at the center, surrounded by eight spheres, which carried the moon, the sun, the stars, and the five planets known at the time: Mercury, Venus, Mars, Jupiter, and Saturn. The planets themselves moved on smaller circles attached to their respective spheres in order to account for their rather complicated observed paths in the sky. The outermost sphere carried the so-called fixed stars, which always stay in the same positions relative to each other but which rotate together across the sky. What lay beyond the last sphere was never made very clear, but it certainly was not part of mankind's observable universe.
Ptolemy's model provided a reasonably accurate system for predicting the positions of heavenly bodies in the sky. But in order to predict these positions correctly, Ptolemy had to make an assumption that the moon followed a path that sometimes brought it twice as close to the Earth as at other times. And that meant that the moon had sometimes to appear twice as big as it usually does. Ptolemy was aware of this flaw but nevertheless his model was generally, although not universally, accepted. It was adopted by the Christian church as the picture of the universe that was in accordance with Scripture. It had the great advantage that it left lots of room outside the sphere of fixed stars for heaven and hell.
A much simpler model, however, was proposed in 1514 by a Polish priest, Nicholas Copernicus. At first, for fear of being accused of heresy, Copernicus published his model anonymously. His idea was that the sun was stationary at the center and that the Earth and the planets moved in circular orbits around the sun. Sadly for Copernicus, nearly a century passed before this idea was to be taken seriously. Then two astronomers—the German, Johannes Kepler, and the Italian, Galileo Galilei—started publicly to support the Copernican theory, despite the fact that the orbits it predicted did not quite match the ones observed. The death of the Aristotelian-Ptolemaic theory came in 1609. In that year Galileo started observing the night sky with a telescope, which had just been invented.
When he looked at the planet Jupiter, Galileo found that it was accompanied by several small satellites, or moons, which orbited around it. This implied that everything did not have to orbit directly around the Earth as Aristotle and Ptolemy had thought. It was, of course, still possible to believe that the Earth was stationary at the center of the universe, but that the moons of Jupiter moved on extremely complicated paths around the Earth, giving the appearance that they orbited Jupiter. However, Copernicus's theory was much simpler.
At the same time, Kepler had modified Copernicus's theory, suggesting that the planets moved not in circles, but in ellipses. The predictions now finally matched the observations. As far as Kepler was concerned, elliptical orbits were merely an ad hoc hypothesis—and a rather repugnant one at that because ellipses were clearly less perfect than circles. Having discovered, almost by accident, that elliptical orbits fitted the observations well, he could not reconcile with his idea that the planets were made to orbit the sun by magnetic forces.
An explanation was provided only much later, in 1687, when Newton published his Principia Mathematica Naturalis Causae. This was probably the most important single work ever published in the physical sciences. In it, Newton not only put forward a theory of how bodies moved in space and time, but he also developed the mathematics needed to analyze those motions. In addition, Newton postulated a law of universal gravitation. This said that each body in the universe was attracted toward every other body by a force which was stronger the more massive the bodies and the closer they were to each other. It was the same force which caused objects to fall to the ground. The story that Newton was hit on the head by an apple is almost certainly apocryphal. All Newton himself ever said was that the idea of gravity came to him as he sat in a contemplative mood, and was occasioned by the fall of an apple.
Newton went on to show that, according to his law, gravity causes the moon to move in an elliptical orbit around the Earth and causes the Earth and the planets to follow elliptical paths around the sun. The Copernican model got rid of Ptolemy's celestial spheres, and with them the idea that the universe had a natural boundary. The fixed stars did not appear to change their relative positions as the Earth went around the sun. It therefore became natural to suppose that the fixed stars were objects like our sun but much farther away. This raised a problem. Newton realized that, according to his theory of gravity, the stars should attract each other; so, it seemed they could not remain essentially motionless. Would they not all fall together at some point?
In a letter in 1691 to Richard Bentley, another leading thinker of his day, Newton argued that this would indeed happen if there were only a finite number of stars. But he reasoned that if, on the other hand, there were an infinite number of stars distributed more or less uniformly over infinite space, this would not happen because there would not be any central point for them to fall to. This argument is an instance of the pitfalls that one can encounter when one talks about infinity.
In an infinite universe, every point can be regarded as the center because every point has an infinite number of stars on each side of it. The correct approach, it was realized only much later, is to consider the finite situation in which the stars all fall in on each other. One then asks how things change if one adds more stars roughly uniformly distributed outside this region. According to Newton's law, the extra stars would make no difference at all to the original ones, and so the stars would fall in just as fast. We can add as many stars as we like, but they will still always collapse in on themselves. We now know it is impossible to have an infinite static model of the universe in which gravity is always attractive.
It is an interesting reflection on the general climate of thought before the twentieth century that no one had suggested that the universe was expanding or contracting. It was generally accepted that either the universe had existed forever in an unchanging state or that it had been created at a finite time in the past, more or less as we observe it today. In part, this may have been due to people's tendency to believe in eternal truths as well as the comfort they found in the thought that even though they may grow old and die, the universe is unchanging.
Even those who realized that Newton's theory of gravity showed that the universe could not be static did not think to suggest that it might be expanding. Instead, they attempted to modify the theory by making the gravitational force repulsive at very large distances. This did not significantly affect their predictions of the motions of the planets. But it would allow an infinite distribution of stars to remain in equilibrium, with the attractive forces between nearby stars being balanced by the repulsive forces from those that were farther away.
However, we now believe such an equilibrium would be unstable. If the stars in some region got only slightly near each other, the attractive forces between them would become stronger and would dominate over the repulsive forces. This would mean that the stars would continue to fall toward each other. On the other hand, if the stars got a bit farther away from each other, the repulsive forces would dominate and drive them farther apart.
Another objection to an infinite static universe is normally ascribed to the German philosopher Heinrich Olbers. In fact, various contemporaries of Newton had raised the problem, and the Olbers article of 1823 was not even the first to contain plausible arguments on this subject. It was, however, the first to be widely noted. The difficulty is that in an infinite static universe nearly every line or side would end on the surface of a star. Thus one would expect that the whole sky would be as bright as the sun, even at night. Olbers's counterargument was that the light from distant stars would be dimmed by absorption by intervening matter. However, if that happened, the intervening matter would eventually heat up until it glowed as brightly as the stars.
The only way of avoiding the conclusion that the whole of the night sky should be as bright as the surface of the sun would be if the stars had not been shining forever, but had turned on at some finite time in the past. In that case, the absorbing matter might not have heated up yet, or the light from distant stars might not yet have reached us. And that brings us to the question of what could have caused the stars to have turned on in the first place.
The beginning of the universe had, of course, been discussed for a long time. According to a number of early cosmologies in the Jewish/ Christian/Muslim tradition, the universe started at a finite and not very distant time in the past. One argument for such a beginning was the feeling that it was necessary to have a first cause to explain the existence of the universe.
Another argument was put forward by St. Augustine in his book, The City of God. He pointed out that civilization is progressing, and we remember who performed this deed or developed that technique. Thus man, and so also perhaps the universe, could not have been around all that long. For otherwise we would have already progressed more than we have.
St. Augustine accepted a date of about 5000 B.C. for the creation of the universe according to the book of Genesis. It is interesting that this is not so far from the end of the last Ice Age, about 10,000 B.C., which is when civilization really began. Aristotle and most of the other Greek philosophers, on the other hand, did not like the idea of a creation because it made too much of divine intervention. They believed, therefore, that the human race and the world around it had existed, and would exist, forever. They had already considered the argument about progress, described earlier, and answered it by saying that there had been periodic floods or other disasters that repeatedly set the human race right back to the beginning of civilization.
When most people believed in an essentially static and unchanging universe, the question of whether of not it had a beginning was really one of metaphysics or theology. One could account for what was observed either way. Either the universe had existed forever, of it was set in motion at some finite time in such a manner as to look as though it had existed forever. But in 1929, Edwin Hubble made the landmark observation that wherever you look, distant stars are moving rapidly away from us. In other words, the universe is expanding. This means that at earlier times objects would have been closer together. In fact, it seemed that there was a time about ten or twenty thousand million years ago when they were all at exactly the same place.
This discovery finally brought the question of the beginning of the universe into the realm of science. Hubble's observations suggested that there was a time called the big bang when the universe was infinitesimally small and, therefore, infinitely dense. If there were events earlier than this time, then they could not affect what happens at the present time. Their existence can be ignored because it would have no observational consequences.
One may say that time had a beginning at the big bang, in the sense that earlier times simply could not be defined. It should be emphasized that this beginning in time is very different from those that had been considered previously. In an unchanging universe, a beginning in time is...
(Continues...)
Excerpted from THE THEORY OF EVERYTHING by Stephen W. Hawking. Copyright © 2002 by New Millennium Press. Excerpted by permission. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
